DESCRIPTION: This is a proposal to examine new methods for variable selection with censored failure times and data that fit the paradigm of the generalized linear models (GLM). These methods are useful in clinical investigations of chronic diseases. In particular, it is proposed to: 1) Develop and study semi-parametric Bayesian methods of variable selection in Cox's proportional hazards regression models for right censored and exact data. Methods for specifying parametric predictive informative prior distributions for the regression coefficients, a nonparametric prior distribution for the baseline hazard rate, and a discrete prior for the model space will be investigated. Properties of the proposed priors and the implied posterior distributions will also be studied. 2) Develop variable selection methods in Bayesian hierarchical GLM. Specification of prior distributions for the regression coefficients and other model parameters arising in the various stages of the hierarchy will be investigated. The main application of this methodology will be to assess institutional and/or geographic variation in multi-center clinical trials. 3) Investigate and implement Gibbs sampling and related Markov chain Monte Carlo (MCMC) techniques to carry out the above proposed methodologies, and write flexible software that will be made publicly available to the practitioner.